Design of extended backstepping sliding mode controller for uncertain chaotic systems

Backstepping technique is one of the tools which provide control Lyapunov functions and control laws for automatic systems. In this paper, strategy design of the extended backstepping sliding mode control (EBSMC) is investigated for uncertain chaotic systems. This technique is applied to achieve chaos control for dynamical systems. The concept of extended systems is used to obtain continuous control input using a backstepping sliding mode. Based on Lyapunov stability theorem, control laws are derived. It guarantees that under the proposed control law, uncertain Genesio chaotic systems can be stabilized to a steady state and can asymptotically track any desired trajectory as well. Numerical simulations are shown to verify the results.